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I didn’t think the puzzle was clear about whether all red and all green sequences were allowed (RRRR and GGGG). But if you do allow them you get the required answer.

This Python program runs in 43ms.

Solution:(a) There were 14 presents around the tree; (b) The colours of the first five presents are: green, green, red, red, green.There are two possible sequences for the solution: G G R R G G G G R G R R R R and G G R R G R G G G G R R R R. They differ at the 6th and 9th positions.